A positive integer $n$ is called naughty if it can be written in the form $n=a^b+b$ with integers $a,b \geq 2$. Is there a sequence of $102$ consecutive positive integers such that exactly $100$ of those numbers are naughty?
Source: Germany VAIMO 2015 - #2
Tags: Integer, positive, consecutive, form, number theory
A positive integer $n$ is called naughty if it can be written in the form $n=a^b+b$ with integers $a,b \geq 2$. Is there a sequence of $102$ consecutive positive integers such that exactly $100$ of those numbers are naughty?